Geodesic
Identification of a polynomial in nonseparated boundary conditions in the case of a multiple zero eigenvalue
Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 13-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the work we discuss the problem of recovering the coefficients of a polynomial in spectral problems with nonseparated boundary conditions by one multiple zero eigenvalue and $n$ nonzero eigenvalues. A uniqueness theorem is proved.
Keywords: eigenvalues, boundary conditions, characteristic determinant. 
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A. M. Akhtyamov; R. R. Kumushbaev. Identification of a polynomial in nonseparated boundary conditions in the case of a multiple zero eigenvalue. Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 13-18. http://geodesic.mathdoc.fr/item/UFA_2015_7_1_a1/

[1] Shkalikov A. ., “Kraevye zadachi dlya obyknovennykh differentsialnykh uravnenii s parametrom v granichnykh usloviyakh”, Trudy seminara im. I. G. Petrovskogo, 9, 1983, 190–229 | MR | Zbl

[2] Kapustin N. Yu., Moiseev E. I., “O spektralnykh zadachakh so spektralnym parametrom v granichnom uslovii”, Differents. uravneniya, 33:1 (1997), 115–119 | MR | Zbl

[3] Akhtyamov A. M., “O vychislenii koeffitsientov razlozhenii po proizvodnym tsepochkam odnoi spektralnoi zadachi”, Matematicheskie zametki, 51:6 (1992), 137–139 | MR | Zbl

[4] Akhtyamov A. M., “O koeffitsientakh razlozhenii po sobstvennym funktsiyam kraevykh zadach s parametrom v granichnykh usloviyakh”, Matematicheskie zametki, 75:4 (2004), 493–506 | DOI | MR | Zbl

[5] S. S. Mirzoev, A. R. Aliev, L. A. Rustamova, “On the Boundary Value Problem with the Operator in Boundary Conditions for the Operator-Differential Equation of Second Order with Discontinous Coefficients”, Zhurn. matem. fiz., anal., geom., 9:2 (2013), 207–226 | MR | Zbl

[6] I. M. Nabiev, A. Sh. Shukurov, “Properties of the spectrum and uniqueness of reconstruction of Sturm–Liouville operator with a spectral parameter in the boundary condition”, Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 40, Special Issue, 332–341 | Zbl

[7] Kh. R. Mamedov, F. Cetinkaya, “Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition”, Bound. Value Probl., 2013, Article ID 183, 16 pp. electronic only, http://link.springer.com/journal/volumesAndIssues/13661 | MR | Zbl

[8] Mamedov Kh. R., “Ob odnoi kraevoi zadache so spektralnym parametrom v granichnykh usloviyakh”, Sib. mat. zhurn., 40:2 (1999), 325–335 | MR | Zbl

[9] E. S. Panakhov, H. Koyunbakan, Ic. Unal, “Reconstruction formula for the potential function of Sturm–Liouville problem with eigenparameter boundary condition”, Inverse Problems in Science and Engineering, 18:1 (2010), 173–180 | DOI | MR | Zbl

[10] M. V. Chugunova, “Inverse spectral problem for the Sturm–Liouville operator with eigenvalue parameter dependent boundary conditions”, Oper. Theory Adv. Appl., 123, Birkhauser, Basel, 2001, 187–194 | MR | Zbl

[11] Van Der Mei K., Pivovarchik V. N., “Obratnaya zadacha Shturma–Liuvillya s zavisyaschimi ot spektralnogo parametra kraevymi usloviyami”, Funkts. analiz i ego prilozheniya, 36:4 (2002), 74–77 | DOI | MR | Zbl

[12] Sadovnichii V. A., Sultanaev Ya. T., Akhtyamov A. M., “Obratnaya zadacha dlya puchka operatorov s neraspadayuschimisya kraevymi usloviyami”, Doklady Akademii nauk, 425:1 (2009), 31–33 | MR | Zbl

[13] G. Freiling, V. Yurko, “Inverse problems for Sturm–Liouville equations with boundary conditions polynomially dependent on the spectral parameter”, Inverse Problems, 26 (2010), 055003, 17 pp. | DOI | MR | Zbl

[14] Akhtyamov A. M., “Ob opredelenii kraevogo usloviya po konechnomu naboru sobstvennykh znachenii”, Differentsialnye uravneniya, 35:8 (1999), 1127–1128 | MR | Zbl

[15] Akhtyamov A. M., Kumushbaev R. R., “Identifikatsiya polinoma v neraspadayuschikhsya kraevykh usloviyakh”, Differentsialnye uravneniya, 48:11 (2012), 1549–1552 | MR | Zbl

[16] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969, 526 pp. | MR

[17] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1976, 576 pp. | MR